Katz centrality

About: Katz centrality is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 77858 citations.

Automated Detection of Influential Patents Using Singular Values

Abstract: Centrality measures such as degree centrality have been utilized to identify influential and important patents in a citation network. However, no existing centrality measures take into consideration information from the change of the similarity matrix. This paper presents a new centrality measure based on the change of a node similarity matrix. The proposed approach gives more intuitive understanding of the finding of the influential nodes. The present study starts off with the assumption that the change of matrix that may result from removing a given node would assess the importance of the node since each node make a contribution to the given similarity matrix between nodes. The various matrix norms using the singular values such as nuclear norm which is the sum of all singular values, are used for calculating the contribution of a given node to a node similarity matrix. In other words, we can obtain the change of matrix norms for a given node after we calculate the singular values for the case of the nonexistence and the case of existence of the node. Then, the node resulting in the largest change (i.e., decrease) of matrix norms can be considered as the most important node. Computation of singular values can be computationally intensive when the similarity matrix size is large. Therefore, the singular value update technique is also developed for the case of the network with large nodes. We compare the performance of our proposed approach with other widely used centrality measures using U.S. patents data in the area of information and security. Experimental results show that our proposed approach is competitive or even performs better compared to existing approaches.

Node Centrality for Continuous-Time Quantum Walks

Abstract: The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a vertex to the influence that its initial phase has on the interference patterns that emerge during the quantum walk evolution. To this end, we make use of the quantum Jensen-Shannon divergence between two suitably defined quantum states. We investigate how the importance varies as we change the initial state of the walk and the Hamiltonian of the system. We find that, for a suitable combination of the two, the importance of a vertex is almost linearly correlated with its degree. Finally, we evaluate the proposed measure on two commonly used networks.

On the limiting behavior of parameter-dependent network centrality measures

Abstract: We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including Katz and subgraph centrality. We show that the parameter can be "tuned" to interpolate between degree and eigenvector centrality, which appear as limiting cases. Our analysis helps explain certain correlations often observed between the rankings obtained using different centrality measures, and provides some guidance for the tuning of parameters. We also highlight the roles played by the spectral gap of the adjacency matrix and by the number of triangles in the network. Our analysis covers both undirected and directed networks, including weighted ones. A brief discussion of PageRank is also given.

Axiomatic Characterization of Game-Theoretic Network Centralities

Abstract: One of the fundamental research challenges in network science is the centrality analysis, i.e., identifying the nodes that play the most important roles in the network. In this paper, we focus on the game-theoretic approach to centrality analysis. While various centrality indices have been proposed based on this approach, it is still unknown what distinguishes this family of indices from the more classical ones. In this paper, we answer this question by providing the first axiomatic characterization of game-theoretic centralities. Specifically, we show that every centrality can be obtained following the game-theoretic approach, and show that two natural classes of game-theoretic centrality can be characterized by two intuitive properties pertaining to Myerson's notion of Fairness.

Computing Top-k Closeness Centrality in Fully-dynamic Graphs

Abstract: Closeness is a widely-studied centrality measure. Since it requires all pairwise distances, computing closeness for all nodes is infeasible for large real-world networks. However, for many applications, it is only necessary to find the k most central nodes and not all closeness values. Prior work has shown that computing the top-k nodes with highest closeness can be done much faster than computing closeness for all nodes in real-world networks. However, for networks that evolve over time, no dynamic top-k closeness algorithm exists that improves on static recomputation. In this paper, we present several techniques that allow us to efficiently compute the k nodes with highest (harmonic) closeness after an edge insertion or an edge deletion. Our algorithms use information obtained during earlier computations to omit unnecessary work. However, they do not require asymptotically more memory than the static algorithms (i. e., linear in the number of nodes). We propose separate algorithms for complex networks (which exhibit the small-world property) and networks with large diameter such as street networks, and we compare them against static recomputation on a variety of real-world networks. On many instances, our dynamic algorithms are two orders of magnitude faster than recomputation; on some large graphs, we even reach average speedups between $10^3$ and $10^4$.